Converter-Driven Electrical Resonance Model of Low-Frequency Oscillation and Synchronous-Frequency Resonance in Grid-Forming Virtual Synchronous Machine

Low-frequency oscillations (LFOs) may pose a risk in grid-forming virtual synchronous machines (GFMVSMs), although the virtual synchronous machine (VSM) can provide inertia and damping support to the grid. This study proposes a new converter-driven electrical resonance (CDER) model to quantitatively analyze the LFO in the GFMVSM system. This CDER model combines converter-driven stability and electrical resonance stability, revisited through the classification and definition of new power systems. The LFO can be intuitively observed and identified by the proposed CDER model from a new perspective of the interaction between the converter-driven part and the electrical resonance part. In addition, the flowchart of the criterion procedure is given for the judgment of LFO from the perspective of the converter-driven electrical resonance. In addition, we propose the oscillatory spread model (OSM) to analyze the abnormal phenomenon in which active-power oscillations do not necessarily cause frequency oscillations. The relationships among the oscillation amplitudes of active and reactive power, frequency, and voltage are quantitatively described by the OSM. Finally, the theoretical modeling method is validated by simulations and experiments. Compared with conventional small-signal/eigenvalue and impedance-based methods, the proposed framework is intended as a complementary mechanism-oriented interpretation: it reorganizes the linearized dynamics into a converter-driven virtual-inertia-damping/low-pass part and an electrical-resonance part so that their interaction can be interpreted explicitly. The OSM further extends earlier frequency-voltage propagation analysis to directional P-Q-E-f transfer paths and quantitatively links analytical gains to measured oscillation-amplitude ratios.